Concurrent with the developments in system identification and increase in scientific data, advances in hardware and software have led to over a one trillion times speed up in mixed-integer optimization (MIO) solvers since 1990 [1]}, [2]}, [3]}. This fact necessitates researchers revisit their preconceptions about the (in)tractability of MIO in machine learning contexts. Indeed, there has been substantial work on viewing the full slate of classical machine learning algorithms under a modern optimization lens [4]}, often yielding state-of-the-art results with practical computational budgets. Most relevant to system identification is the recent progress on high-dimensional sparse regression which solves the NP-hard feature selection problem exactly [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}. In addition to superior performance, these modern formulations inherit the full generality of MIO, empowering domain experts with a rich modeling language to express a vast range of model desiderata as arbitrary linear, quadratic, and semidefinite constraints on both the coefficients and sparsity structure.
